Handling Networks: Graph Theory

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Distinguishes between subgraphs and induced subgraphs in graph theory, illustrating the construction of minimal spanning trees.

Introduces the basics of graphs and networks, covering definitions, paths, trees, flows, circulation, and spanning trees.

Explores directed networks with asymmetric relationships and hypergraphs that generalize graphs by allowing edges to connect any subset of nodes.

Covers embedding graphs into trees with a focus on minimizing distortion and Bartal Tree embeddings.

Explores statistical analysis of network data, covering noisy sampled networks, likelihood estimation, multilayer networks, and directed networks.

Explores Prim's algorithm for minimum spanning trees and introduces the Traveling Salesman Problem.

Covers graphical models for probability distributions and factor graphs representation.

Explores scale-free networks, power laws, preferential attachment, and network assortativity.

Explores graph theory in brain connectomics, MRI applications, network analysis relevance, and individual fingerprinting.